00240 �e77afc2d2959074307e464c36ca12e

242

Yander Wiel

on the ąuality of measurements the device can produce and they do not presently concem the engineer who manages the lab. Naturally, nobody involved with this process wants to be notified every time one of the 5 measuring devices causes a signal on a traditional EWMA chart.

Large shifts in power (e.g., 0.5 dB or morę), however, significantly degrade measurement precision and should be detected as soon as possible. For example, one day the power on one device suddenly dropped about 3 dB. This probably happened because someone bumped the splice between the input port on the measuring device and a short jumper cable which is considered part of the measuring system. If laser power were not monitored the ąuality of measurements produced that day would be significantly degraded and no one would know.

In this example widening the control limits on the EWMA chart is a sensible approach to monitoring output power. A Shewhart individuals chart with wide limits would be eąually effective. The particular monitoring scheme used is not critical and choosing appropriate control limits is mostly a matter of engineering judgement. Average run lengths and statistical performance properties of the monitoring scheme will play a very smali role, if any.

Widening the control limits makes sense in this example because the nominał amount of variation in power is at least an order of magnitude smaller than what can be tolerated without substantively harming measurement ąuality. Such a simple solution is not appropriate in the r xt example.

Example 2—wide limits might obscure important process changes The top panel of Figurę 2 shows data from consecutive batches of polymer from a process studied by Vander Wiel, Tucker, Faltin and Doganaksoy (1992). The plot shows 109 viscosity measurements corrected for the efifect of catalyst changes which are routinely madę in this process. In other words, the viscosities are approximations of what would have resulted if the level of catalyst had remained fixed. Clearly, with no catalyst adjustments the process will wander. Viscosity deviations from target are used to adjust the amount of catalyst loaded into futurę batches. This feedback loop transfers the wandering process disturbance from the viscosity measurements to the catalyst level and thus reduces the variability in viscosity.

Removing sources of variation rather than transferring them to other variables is considered vital to the continued yiability of this product. Reducing the process standard deviation by even 5% could potentially save millions of dollars per year in waste and extra processing costs. Thus, it is important to monitor this process for unexpected changes in viscosity that might have “assignable causes.” For example, in the top panel of Figurę 2 a downward